The quadratic function p(x) = x² + 3x - 154 accurately represents p(x) with solutions -14 and 11, distinguishing it from other options.
The solutions of the quadratic equation p(x) = 0 are the values of x for which the equation is true. Given that the solutions are -14 and 11, we can use these values to determine which function could represent p(x).
The factored form of a quadratic equation is p(x) = (x - r₁)(x - r₂), where r₁ and r₂ are the roots or solutions of the equation. For the given solutions, -14 and 11, the factored form would be p(x) = (x + 14)(x - 11).
Now, let's expand this expression to check which function matches:
p(x) = (x + 14)(x - 11) = x² + 3x - 154
Comparing this with the given options:
A. p(x) = x² - 3x - 154 - Incorrect
B. p(x) = x² - 14x + 11 - Incorrect
C. p(x) = x² + 14x + 11 - Incorrect
D. p(x) = x² + 3x - 154 - Correct
Therefore, the function that could represent p(x) with roots -14 and 11 is:
D. p(x) = x² + 3x - 154